Evaluate the definite integral. $\int^{-8}_{0}\left(-4\sqrt[3]{x}\right)\,dx = $
First, use the power rule: $\begin{aligned}\int^{-8}_{0}\left(-4\sqrt[3]{x}\right)\,dx~&=~\int^{-8}_{0}\left(-4x^\frac13\right)\,dx \\&=(-3x^\frac43)\Bigg|^{-8}_{0}\end{aligned}$ Second, plug in the limits of integration: $[-3\cdot({-8})^{\frac43}]-[-3\cdot0^{\frac43}] = -48-0 = -48$. The answer: $\int^{-8}_{0}\left(-3\sqrt[3]{x}\right)\,dx~=~-48$